›› 2018, Vol. 39 ›› Issue (S1): 477-487.doi: 10.16285/j.rsm.2018.0285

• 数值分析 • 上一篇    下一篇

基于C2阶连续函数的广义Hoek-Brown强度准则屈服面与塑性势面棱角圆化方法

周兴涛1, 2,盛 谦1, 2,崔 臻1,朱泽奇1,胡之锋1,马亚丽娜1, 2   

  1. 1. 中国科学院武汉岩土力学研究所 岩土力学与工程国家重点实验室,湖北 武汉 430071;2. 中国科学院大学,北京 100049
  • 收稿日期:2018-03-01 出版日期:2018-07-20 发布日期:2018-09-02
  • 作者简介:周兴涛,男,1987年生,博士研究生,主要从事地下工程抗震及边坡动力稳定性方面研究工作
  • 基金资助:

    国家重点基础研究发展计划(973)项目(No. 2015CB057905);国家自然科学基金资助项目(No. 51779253,No. 41672319);湖北省自然科学基金资助项目(No. 2017CFB725)。

C2 continuous approximation to generalized Hoek-Brown strength criterion yield surface and plastic potential surface

ZHOU Xing-tao1, 2, SHENG Qian1, 2, CUI Zhen1, ZHU Ze-qi1, HU Zhi-feng1, MA Ya-lina1,2   

  1. 1. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China; 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2018-03-01 Online:2018-07-20 Published:2018-09-02
  • Supported by:

    The work was supported by the National Program on Key Basic Research Project of China (973 Program) (2015CB057905),the National Natural Science Foundation of China(51779253, 41672319), and the Hubei Natural Science Foundation(2017CFB725).

摘要: Hoek-Brown强度准则的屈服面与塑性势面在棱角处导数无定义,具有数值奇异性,采用圆角进行光滑过渡只能满足一阶导数连续性,而二阶导数仍然无定义,使得棱边上一致切线模量矩阵无法正确计算,导致有限元总体平衡方程组Newton-Raphson隐式迭代二阶收敛性丧失。提出基于C2阶连续函数的广义Hoek-Brown准则屈服面与塑性势面棱角圆化方法,使得棱角处函数曲面二阶连续可导,棱边上一致切线模量矩阵可精确计算。基于ABAQUS数值开发平台,采用FORTRAN语言编制Hoek-Brown准则理想弹塑性UMAT用户子程序,通过数值算例验证所提方法的正确性。

关键词: 广义Hoek-Brown强度准则, 屈服函数与塑性势函数, C2阶连续函数, 圆化

Abstract: Derivative is not defined at the edge corners of yield and plastic potential surfaces based on the generalized Hoek-Brown strength criterion and numerical singularity has been caused there. Smooth transitions with circular surface only satisfy the first derivative continuity; the second derivative is still undefined on the edges; so that the consistent tangent modulus can not be calculated correctly there. The implicit solution of nonlinear equilibrium equations in finite element method(FEM) with Newton-Raphson method is unable to achieve full quadratic convergence. C2 continuous rounding of yield and plastic potential surfaces in the π-plane has been introduced; so that the surfaces can be second-order continuous derivative on the edges; and the consistent tangent modulus matrix can be calculated accurately. Subroutine UMAT for the generalized Hoek-Brown linear elastic-perfectly plastic constitutive model has been coded with FORTRAN in ABAQUS software. Numerical examples are used to verify the correctness of the proposed method.

Key words: generalized Hoek-Brown strength criterion, yield and plastic potential functions, C2 continuous function, rounding

中图分类号: 

  • P642

[1] 马林建,阳 发,王明洋,李 増,. 考虑应变率效应的广义Hoek-Brown动态强度准则[J]. , 2017, 38(S2): 27-32.
[2] 童 磊,谢康和,程永锋,卢萌盟,王 坤. 考虑椭圆化地层变形影响的浅埋隧道弹性解[J]. , 2009, 30(2): 393-398.
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